Stitz-Zeager_College_Algebra_e-book

S 3 4 solution 1 even though we are not explicitly

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Unformatted text preview: minutes and 7 seconds (which is 127 seconds) the period T = 1 (127) = 127 seconds. Hence, the 2 2 4π angular frequency is ω = 2π = 127 radians per second. Putting these two pieces of information T 4π together, we have that y = 64 sin 127 t describes the y -coordinate on the Giant Wheel after t seconds, assuming it is centered at (0, 0) with t = 0 corresponding to the point Q. In order to ﬁnd an expression for h, we take the point O in the ﬁgure as the origin. Since the base of the Giant Wheel ride is 8 feet above the ground and the Giant Wheel itself has a radius of 64 feet, its center is 72 feet above the ground. To account for this vertical shift upward,4 we add 72 to our formula 4π for y to obtain the new formula h = y + 72 = 64 sin 127 t + 72. Next, we need to adjust things so that t = 0 corresponds to the point P instead of the point Q. This is where the phase comes into play. Geometrically, we need to shift the angle θ in the ﬁgure back π radians. From Section 10.2.1, 2 4π we know θ = ωt = 12...
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